Question

Differentiate the following w.r.t.x:
${\tan }^{-1}\left(\frac{\cos x+\sin x}{\cos x-\sin x}\right)$

Answer 1

$y={\tan }^{-1}\left(\frac{\cos x+\sin x}{\cos x-\sin x}\right)$

$y={\tan }^{-1}\left(\frac{1+\tan x}{1-\tan x}\right)$

$y={\tan }^{-1}\tan (\frac{\pi }{4}+x)$

$y=\frac{\pi }{4}+x$

$\frac{dy}{dx}=1$